Integer multiplication and division rules

Learning Objectives Identify positive and negative integers. State the rules for multiplying two integers with the same sign. State the rules for multiplying two integers with different signs. Apply the rules for dividing two integers with the same sign. Apply the rules for dividing two integers with different signs. Accurately calculate products and quotients of integers. Solve multi-step problems involving integer multiplication and division. Ever wonder how temperatures can drop below zero or how debt accumulates? 📉 Understanding how to multiply and divide positive and negative numbers helps us make sense of these real-world situations! In this lesson, you'll learn the essential rules for multiplying and dividing integers. Mastering these operations is crucial fo...

TermDefinitionExample IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero. Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...The numbers -7, 0, and 15 are all integers. Positive IntegerAn integer greater than zero. These numbers are usually written without a sign or with a '+' sign.5, 12, 100 are positive integers. Negative IntegerAn integer less than zero. These numbers are always written with a '-' sign.-3, -8, -50 are negative integers. ProductThe result of multiplying two or more numbers.The product of 4 and -2 is -8. QuotientThe result of dividing one number by another.The quotient of -10 and 2 is -5. Absolute ValueThe distance of a number from zero on the number line, always expressed as a positive value. It's denoted by vertica...

Multiplication/Division Rule: Same Signs $$(+a) \times (+b) = +ab$$ $$(+a) \div (+b) = +\frac{a}{b}$$ $$(-a) \times (-b) = +ab$$ $$(-a) \div (-b) = +\frac{a}{b}$$ When you multiply or divide two integers with the same sign (both positive or both negative), the result is always a positive number. Multiplication/Division Rule: Different Signs $$(+a) \times (-b) = -ab$$ $$(-a) \times (+b) = -ab$$ $$(+a) \div (-b) = -\frac{a}{b}$$ $$(-a) \div (+b) = -\frac{a}{b}$$ When you multiply or divide two integers with different signs (one positive and one negative), the result is always a negative number.